By Donald C. Benson
Книга A Smoother Pebble: Mathematical Explorations A Smoother Pebble: Mathematical Explorations Книги Математика Автор: Donald C. Benson Год издания: 2003 Формат: pdf Издат.:Oxford collage Press Страниц: 280 Размер: 11,1 ISBN: 0195144368 Язык: Английский0 (голосов: zero) Оценка:This booklet takes a unique examine the themes of college mathematics--arithmetic, geometry, algebra, and calculus. during this walk at the mathematical beach we are hoping to discover, quoting Newton, "...a smoother pebble or a prettier shell than ordinary..." This publication assembles a suite ofmathematical pebbles which are very important in addition to attractive.
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Extra resources for A Smoother Pebble: Mathematical Explorations
5. A square wave. square wave together with harmonics of this fundamental frequency with suitably chosen amplitudes and phase angles. 6 For an acoustical square wave, the approximating sine waves are partials. 1. Frequency. For a square wave, the frequencies of the partials are odd multiples only of the fundamental. Recall that the clarinet also has principally odd harmonic partials. There are websites where the sound of a square wave can be heard. The sound of a square wave is vaguely like a clarinet, but far from pleasant—the ugly cousin of the clarinet.
176) argues that certain propositions concerning ratios in Book X cannot easily be derived from Eudoxus's theory, and that, therefore, Theaetetus must have used a different definition of ratio using a method called anthyphairesis; we will call it back-and-forth subtraction, or simply BAFS. 1, the Axiom of Archimedes, we see that, given a greater magnitude A and smaller magnitude B, there must be largest multiple of B that does not exceed A. We state this more precisely in the following proposition, which is currently known as the division algorithm?
The critical bandwidth underlies the perception of consonance and dissonance. The interplay of consonance and dissonance is one source of music's endless fascination. Consonance versus dissonance We hear tinkling, pounding, buzzing, whirring, roaring, and, most important of all, the sound of speech. However, our concern here is mainly sound as it is perceived by musicians and their listeners. More particularly, we consider how we hear two simultaneous sustained musical tones. Our ears recognize that the pair of tones C-G has the same character as D-A; we say both are fifths.
A Smoother Pebble: Mathematical Explorations by Donald C. Benson